Biomedical subjects

S Gueron

Publications and source records attributed to S Gueron.

10 recordsLinked to original sources

PubMed2001

A three-dimensional model for ciliary motion based on the internal 9+2 structure.

Here we present, to our knowledge, the first modelling platform that enables simulations of three-dimensional (3D) motion of multicilia arrays at a detailed level. It consists of three building blocks: (i) geometric equations for tracking the 3D motion of the cilia, (ii) a hydrodynamic description of the ciliary system, and (iii) model equations for the internal bend generating based on the 9 + 2 structure. The model generates seemingly realistic 3D beat patterns and demonstrates metachronal coordination that evolves autonomously as a result of the hydrodynamic coupling between the cilia. We study the effect of the twisting motion within the cilia and propose a conjecture on a possible role of the radial spokes system.

Cilia↗

PubMed1999

Energetic considerations of ciliary beating and the advantage of metachronal coordination.

The internal mechanism of cilia is among the most ancient biological motors on an evolutionary scale. It produces beat patterns that consist of two phases: during the effective stroke, the cilium moves approximately as a straight rod, and during the recovery stroke, it rolls close to the surface in a tangential motion. It is commonly agreed that these two phases are designed for efficient functioning: the effective stroke encounters strong viscous resistance and generates thrust, whereas the recovery stroke returns the cilium to starting position while avoiding viscous resistance. Metachronal coordination between cilia, which occurs when many of them beat close to each other, is believed to be an autonomous result of the hydrodynamical interactions in the system. Qualitatively, metachronism is perceived as a way for reducing the energy expenditure required for beating. This paper presents a quantitative study of the energy expenditure of beating cilia, and of the energetic significance of metachronism. We develop a method for computing the work done by model cilia that beat in a viscous fluid. We demonstrate that for a single cilium, beating in water, the mechanical work done during the effective stroke is approximately five times the amount of work done during the recovery stroke. Investigation of multicilia configurations shows that having neighboring cilia beat metachronally is energetically advantageous and perhaps even crucial for multiciliary functioning. Finally, the model is used to approximate the number of dynein arm attachments that are likely to occur during the effective and recovery strokes of a beat cycle, predicting that almost all of the available dynein arms should participate in generating the motion.

Cilia↗

PubMed1998

Computation of the internal forces in cilia: application to ciliary motion, the effects of viscosity, and cilia interactions.

This paper presents a simple and reasonable method for generating a phenomenological model of the internal mechanism of cilia. The model uses a relatively small number of parameters whose values can be obtained by fitting to ciliary beat shapes. Here, we use beat patterns observed in Paramecium. The forces that generate these beats are computed and fit to a simple functional form called the "engine." This engine is incorporated into a recently developed hydrodynamic model that accounts for interactions between neighboring cilia and between the cilia and the surface from which they emerge. The model results are compared to data on ciliary beat patterns of Paramecium obtained under conditions where the beats are two-dimensional. Many essential features of the motion, including several properties that are not built in explicitly, are shown to be captured. In particular, the model displays a realistic change in beat pattern and frequency in response to increased viscosity and to the presence of neighboring cilia in configurations such as rows of cilia and two-dimensional arrays of cilia. We found that when two adjacent model cilia start beating at different phases they become synchronized within several beat periods, as observed in experiments where two flagella are brought into close proximity. Furthermore, examination of various multiciliary configurations shows that an approximately antiplectic wave pattern evolves autonomously. This modeling evidence supports earlier conjectures that metachronism may occur, at least partially, as a self-organized phenomenon due to hydrodynamic interactions between neighboring cilia.

Animals↗

PubMed1997

Cilia internal mechanism and metachronal coordination as the result of hydrodynamical coupling.

We present a simple but realistic model for the internal bend-generating mechanism of cilia, using parameters obtained from the analysis of data of the beat of a single cilium, and incorporate it into a recently developed dynamical model. Comparing the results to experimental data for two-dimensional beats, we demonstrate that the model captures the essential features of the motion, including many properties that are not built in explicitly. The beat pattern and frequency change in response to increased viscosity and the presence of neighboring cilia in a realistic fashion. Using the model, we are able to investigate multicilia configurations such as rows of cilia and two-dimensional arrays of cilia. When two adjacent model cilia start beating at different phase, they synchronize within two cycles, as observed in experiments in which two flagella beating out of phase are brought close together. Examination of various multicilia configurations shows that metachronal patterns (i. e., beats with a constant phase difference between neighboring cilia) evolve autonomously. This provides modeling evidence in support of the conjecture that metachronism may occur as a self-organized phenomenon due to hydrodynamical interactions between the cilia.

Cilia↗

PubMed1995

Dopamine modulation of two subthreshold currents produces phase shifts in activity of an identified motoneuron.

1. The lateral pyloric (LP) neuron is a component of the 14-neuron pyloric central pattern generator in the stomatogastric ganglion of the spiny lobster, Panulirus interruptus. In the pyloric rhythm, this neuron fires rhythmic bursts of action potentials whose phasing depends on the pattern of synaptic inhibition from other network neurons and on the intrinsic postinhibitory rebound properties of the LP cell itself. Bath-applied dopamine excites the LP cell and causes its activity to be phase advanced in the pyloric motor pattern. At least part of this modulatory effect is due to dopaminergic modulation of the intrinsic rate of postinhibitory rebound in the LP cell. 2. The LP neuron was isolated from all detectable synaptic input. We measured the rate of recovery after 1-s hyperpolarizing current injections of varying amplitudes, quantifying the latency to the first spike following the hyperpolarizing prepulse and the interval between the first and second action potentials. Dopamine reduced both the first spike latency and the first interspike interval (ISI) in the isolated LP neuron. During the hyperpolarizating pre-steps, the LP cell showed a slow depolarizing sag voltage that was enhanced by dopamine. 3. We used voltage clamp to analyze dopamine modulation of subthreshold ionic currents whose activity is affected by hyperpolarizing prepulses. Dopamine modulated the transient potassium current IA by reducing its maximal conductance and shifting its voltage dependence for activation and inactivation to more depolarized voltages. This outward current is normally transiently activated after hyperpolarization of the LP cell, and delays the rate of postinhibitory rebound; by reducing IA, dopamine thus accelerates the rate of rebound of the LP neuron. 4. Dopamine also modulated the hyperpolarization-activated inward current Ih by shifting its voltage dependence for activation 20 mV in the depolarizing direction and accelerating its rate of activation. This enhanced inward current helps accelerate the rate of rebound in the LP cell after inhibition. 5. The relative roles of Ih and IA in determining the first spike latency and first ISI were explored using pharmacological blockers of Ih (Cs+) and IA [4-aminopyridine (4-AP)]. Blockade of Ih prolonged the first spike latency and first ISI, but only slightly reduced the net effect of dopamine. In the continued presence of Cs+, blockade of IA with 4-AP greatly shortened the first spike latency and first ISI. Under conditions where both Ih and IA were blocked, dopamine had no additional effect on the LP cell. 6. We used the dynamic clamp technique to further study the relative roles of IA and Ih modulation in dopamine's phase advance of the LP cell. We blocked the endogenous Ih with Cs+ and replaced it with a simulated current generated by a computer model of Ih. The neuron with simulated Ih gave curves relating the hyperpolarizing prepulse amplitude to first spike latency that were the same as in the untreated cell. Changing the computer parameters of the simulated Ih to those induced by dopamine without changing IA caused only a slight reduction in first spike latency, which was approximately 20% of the total reduction caused by dopamine in an untreated cell. Bath application of dopamine in the presence of Cs+ and simulated Ih (with control parameters) allowed us to determine the effect of altering IA but not Ih: this caused a significant reduction in first spike latency, but it was still only approximately 70% of the effect of dopamine in the untreated cell. Finally, in the continued presence of dopamine, changing the parameters of the simulated Ih to those observed with dopamine reduced the first spike latency to that seen with dopamine in the untreated cell. 7. We generated a mathematical model of the lobster LP neuron, based on the model of Buchholtz et al. for the crab LP neuron.

Animals↗

PubMed1995

Dopamine modulation of transient potassium current evokes phase shifts in a central pattern generator network.

Bath application of dopamine modifies the rhythmic motor pattern generated by the 14 neuron pyloric network in the stomatogastric ganglion of the spiny lobster, Panulirus interruptus. Among other effects, dopamine excites many of the pyloric constrictor (PY) neurons to fire at high frequency and phase-advances the timing of their activity in the motor pattern. These responses arise in part from direct actions of dopamine to modulate the intrinsic electrophysiological properties of the PY cells, and can be studied in synaptically isolated neurons. The rate of rebound following a hyperpolarizing prestep and the spike frequency during a subsequent depolarization are both accelerated by dopamine. Based on theoretical simulations, Hartline (1979) suggested that the rate of postinhibitory rebound in stomatogastric neurons could vary with the amount of voltage-sensitive transient potassium current (IA). Consistent with this prediction, we found that dopamine evokes a net conductance decrease in synaptically isolated PY neurons. In voltage clamp, dopamine reduces IA, specifically by reducing the amplitude of the slowly inactivating component of the current and shifting its voltage activation curve in the depolarized direction. 4-Aminopyridine, a selective blocker of IA in stomatogastric neurons, mimics and occludes the effects of dopamine on isolated PY neurons. A conductance-based mathematical model of the PY neuron shows appropriate changes in activity upon quantitative modification of the IA parameters affected by dopamine. These results demonstrate that dopamine excites and phase-advances the PY neurons in the rhythmic pyloric motor pattern at least in part by reducing the transient K+ current, IA.

4-Aminopyridine↗

PubMed1993

Mapping the dynamics of a bursting neuron.

The anterior burster (AB) neuron of the lobster stomatogastric ganglion displays varied rhythmic behavior when treated with neuromodulators and channel-blocking toxins. We introduce a channel-based model for this neuron and show how bifurcation analysis can be used to investigate the response of this model to changes of its parameters. Two dimensional maps of the parameter space of the model were constructed using computational tools based on the theory of nonlinear dynamical systems. Changes in the intrinsic firing and oscillatory properties of the model AB neuron were correlated with the boundaries of Hopf and saddle-node bifurcations on these maps. Complex rhythmic patterns were observed, with a bounded region of the parameter plane producing bursting behavior of the model neuron. Experiments were performed by treating an isolated AB cell with 4-aminopyridine which selectively reduces gA, the conductance of the transient potassium channel. The model accurately predicts the qualitative changes in the neuronal voltage oscillations that are observed over a range of reduction of gA in the neuron. These results demonstrate the efficacy of dynamical systems theory as a means of determining the varied oscillatory behaviors inherent in a channel-based neural model. Further, the maps of bifurcations provide a useful tool for determining how these behaviors depend upon model parameters and comparing the model to a real neuron.

4-Aminopyridine↗

PubMed1993

Simulations of three-dimensional ciliary beats and cilia interactions.

A new set of equations describing the time evolution of torsion and curvature for an inextensible curve is developed. Combined with our recently developed Slender Body Theory approach to such problems, these equations were applied to simulate three-dimensional ciliary beats, while allowing for cilia interactions. The computer animation technique, which was originally designed to display two-dimensional beats, has been enhanced to accommodate the new three-dimensional results.

Animals↗

PubMed1989

A model of herd grazing as a travelling wave, chemotaxis and stability.

Possible constitutive models are examined for the formation of a herd, under the assumption that a herd forms a travelling wave while grazing. Under quite general conditions, it is found that the only possibility for a travelling wave is a balance between food seeking and natural dispersion, such as in chemotaxis. The stability of the travelling wave previously conjectured, is shown both for one- and two-dimensional perturbations.

Animals↗

PubMedDate not supplied

The dynamics of group formation.

A general continuous model is presented for animal group size distribution. Attention is restricted to a fixed size population divided into groups of various dynamic sizes, but the approach extends easily to populations of variable size. The basic idea is to relate group size distribution to two functions, the (density-dependent) rates of fusion and fission. These functions can be estimated from data and can ultimately be related to the behavior of individuals and the dynamics of groups. For various functional forms, the stationary distributions of group sizes are sought. In several prototype cases, the stationary distribution has a peak value, the "most frequent group size," which emerges endogenously from the dynamics. The authors determine when such a peak emerges and more generally show the existence and uniqueness of the stationary distribution. Stability of stationary solutions is discussed. Progress is shown, but a general treatment remains refractory.

Animals↗